A nine-story steel frame building has been subjected to an extensive ser of forced resonance tests. Seven translational and three torsional modes were investigated in detail. A mode in which the floor slabs vibrated horizontally as free-free beams was excited as well. Stiffness and damping matrices were calculated from the experimentally determined modal properties. Damping values were found to be considerably lower than those usually mentioned in the literature. The lowest translational modes in the two principal directions of the building had damping values of approximately 0.5%. The second lowest translational modes had damping values of approximately 1.0%. Damping was found to increase linearly with resonant frequencies. Consistent, but small increases in damping values were found as the amplitude was increased. The damping mechanism is well represented by relative dashpots.